Correlation Length Scale Research Articles

Sedimentation dynamics of passive particles in dilute bacterial suspensions: emergence of bioconvection

Microorganisms are ubiquitous in nature and technology. They inhabit diverse environments, ranging from small river tributaries and lakes, to oceans, as well as wastewater treatment plants and food manufacturing. In many of these environments, microorganisms coexist with settling particles. Here, we investigate the effects of microbial activity (swimming E. coli) on the settling dynamics of passive colloidal particles using particle tracking methods. Our results reveal the existence of two distinct regimes in the correlation length scale ( $L_u$ ) and the effective diffusivity of the colloidal particles ( $D_{eff}$ ), with increasing bacterial concentration ( $\phi _b$ ). At low $\phi _b$ , the parameters $L_u$ and $D_{eff}$ increase monotonically with increasing $\phi _b$ . Beyond critical $\phi _b$ , a second regime is found where both $D_{eff}$ and $L_u$ are independent of $\phi _b$ . We demonstrate that the transition between these regimes is characterized by the emergence of bioconvection. We use experimentally measured particle-scale quantities $L_u$ and $D_{eff}$ to predict the critical bacterial concentration for the diffusion–bioconvection transition.

Mean-field analysis of the glassy dynamics of an elastoplastic model of super-cooled liquids

We present a mean-field theory of a coarse-grained model of a super-cooled liquid in which relaxation occurs via local plastic rearrangements. Local relaxation can be induced by thermal fluctuations or by the long-range elastic consequences of other rearrangements. We extract the temperature dependence of both the relaxation time and the length scale of dynamical correlations. We find two dynamical regimes. First, a regime in which the characteristic time and length scales diverge as a power law at a critical temperature T c . This regime is found by an approximation that neglects activated relaxation channels, which can be interpreted as akin to the one found by the mode-coupling transition of glasses. In reality, only a crossover takes place at T c . The residual plastic activity leads to a second regime characterised by an Arrhenius law below T c . In this case, we show that the length scale governing dynamical correlations diverges as a power law as , and is logarithmically related to the relaxation time.

Arctic Freeboard and Snow Depth From Near‐Coincident CryoSat‐2 and ICESat‐2 (CRYO2ICE) Observations: A First Examination of Winter Sea Ice During 2020–2022

AbstractIn the summer of 2020, ESA changed the orbit of CryoSat‐2 to align periodically with NASA's ICESat‐2 mission, a campaign known as CRYO2ICE, which allows for near‐coincident CryoSat‐2 and ICESat‐2 observations in space and time over the Arctic until summer 2022, where the CRYO2ICE Antarctic campaign was initiated. This study investigates the Arctic CRYO2ICE radar and laser freeboards acquired by CryoSat‐2 and ICESat‐2, respectively, during the winter seasons of 2020–2022, and derives snow depths from their differences along the orbits. Along‐track snow depth observations can provide high‐resolution snow depth distributions which are vital for air‐ice‐ocean heat and momentum transfer, understanding light transmission, and snow‐ice‐interactions. Generally, ICESat‐2 is backscattered at a surface above the elevation of the CryoSat‐2 signal. CRYO2ICE snow depths are thinner than the daily model‐ or passive‐microwave‐based snow depth composites used for comparison, with differences being most pronounced in the Atlantic and Pacific Arctic. Satellite‐derived and model‐based snow estimates show similar seasonal accumulation over first‐year ice, but CRYO2ICE has limited seasonal accumulation over multi‐year ice which is linked to a slow increase in ICESat‐2, and to some extent CryoSat‐2, freeboards. We present a first estimation of spaceborne along‐track snow depth estimates with average uncertainty of 10–11 ± 2–3 cm for 7‐km segments, with random and systematic contributions of 7 and 4 cm. These observations show the potential for along‐track dual‐frequency observations of snow depth from the future Copernicus mission CRISTAL; but they also highlight uncertainties in radar penetration and the correlation length scales of snow topography that still require further research.

Influence of swift heavy ion irradiation on structure and morphology of La0.25Pr0.375Ca0.375MnO3 film

The effects of Ag15+ (120 MeV) swift heavy ion (SHI) irradiation on the structural and morphological properties of epitaxial La0.25Pr0.375Ca0.375MnO3 (LPCMO) thin films were investigated by x-ray scattering and atomic force microscopy (AFM) techniques. LPCMO films of thickness ∼ 280 Å were irradiated with an Ag15+ ion beam at different fluences of 1 × 1011, 5 × 1011, and 1 × 1012 ions cm−2. XRD results suggested the development of the tensile stress along the out-of-plane direction of the LPCMO film upon ion irradiation, which increases on increasing the ion fluence. The morphology of the film was also modified with the irradiation and an increase in the fluence of the ion beam enhanced the in-plane height-height correlation length scale (grain size) with a loss of the fractal behaviours. The linear variation of microstrain with ion irradiation fluence in thin LPCMO film can be considered for a possible strain-driven application in modifying functional properties of such a phase separated complex oxide.

A simplified potential source density function based on predefined discretization

The potential source contribution function (PSCF) method is widely used in the analysis of air pollutant source areas, but it also faces several limitations. To address such limitations, the potential source density function (PSDF) method was developed based on Gaussian process regression (GPR). However, the PSDF model requires more computational resources than the PSCF model. Here, we present an enhanced model with improved speed. We discretized the PSDF method by assigning a predetermined spatial correlation between cells through a priori known correlation length scale. The time taken was reduced by 25–30% from that of the original PSDF method, while the values representing the air pollution sources exhibited only a slight difference from the original ones. Our new method reduces the time required for computational calculations, measures potential sources with comparable precision, and ensures the reliability and source intensity of the results.

Iterative ensemble smoothing scheme for reservoir history matching with unknown observation error covariance

Ensemble-based smoothers are well-known data assimilation tools in reservoir applications, including history matching and geophysical inversion. They entail the knowledge of the covariance of observation errors, which, however, is often poorly known in real applications and commonly estimated subjectively on the basis of a diagonal structure. This neglects the correlations within the observation errors, which may deteriorate the quality of the model estimates. Herein, we relaxed the independent observational error assumption by considering a nondiagonal structure for the covariance. Given that all the elements in the covariance matrix could not be estimated given a limited amount of data, which is typically the case in practice, we reduced the number of degrees of freedom by parameterizing this covariance with two scalar parameters, one for error variance and the other for error correlation length–scale. We then estimated these parameters together with the model variables using a hybrid algorithm that combined a variational Bayesian approach with particle filters and an ensemble-based smoother. The proposed approach was validated with a linear Gaussian model and a nonlinear reservoir flow model. The results clearly demonstrate the potential of the proposed method in effectively addressing the uncertainty of observations in the history-matching process.

Impacts of radar forward operator on convective-scale data assimilation and short-term forecasts

The current study utilizes the operational data assimilation system of Deutscher Wetterdienst (DWD) to investigate the impacts of improved radar forward operator. First of all, it is shown that for experiments in which both conventional and radar data are assimilated and the latent heat nudging (LHN) is applied, the one with improved operator (i.e., with improved Mie-scattering scheme and accounting for beam broadening effect and etc.) exhibits neutral impacts on short-term forecasts. However, in subsequent experiments, in which conventional data are not assimilated and the LHN is switched off, the one with improved operator not just reduces representation error during data assimilation cycles but also enhances the short-term forecast skills. In addition, it is found that the subsequent experiments result in much shorter observation error correlation length scales for radar reflectivity data, indicating that the application of the LHN or assimilation of conventional data may increase the length scales.

Multivariate Emulation of Kilometer-Scale Numerical Weather Predictions with Generative Adversarial Networks: A Proof of Concept

Abstract Emulating numerical weather prediction (NWP) model outputs is important to compute large datasets of weather fields in an efficient way. The purpose of the present paper is to investigate the ability of generative adversarial networks (GANs) to emulate distributions of multivariate outputs (10-m wind and 2-m temperature) of a kilometer-scale NWP model. For that purpose, a residual GAN architecture, regularized with spectral normalization, is trained against a kilometer-scale dataset from the AROME Ensemble Prediction System (AROME-EPS). A wide range of metrics is used for quality assessment, including pixelwise and multiscale Earth-mover distances, spectral analysis, and correlation length scales. The use of wavelet-based scattering coefficients as meaningful metrics is also presented. The GAN generates samples with good distribution recovery and good skill in average spectrum reconstruction. Important local weather patterns are reproduced with a high level of detail, while the joint generation of multivariate samples matches the underlying AROME-EPS distribution. The different metrics introduced describe the GAN’s behavior in a complementary manner, highlighting the need to go beyond spectral analysis in generation quality assessment. An ablation study then shows that removing variables from the generation process is globally beneficial, pointing at the GAN limitations to leverage cross-variable correlations. The role of absolute positional bias in the training process is also characterized, explaining both accelerated learning and quality-diversity trade-off in the multivariate emulation. These results open perspectives about the use of GAN to enrich NWP ensemble approaches, provided that the aforementioned positional bias is properly controlled.

Statistics of the cuprate pairon states on a square lattice

In this paper the fundamental parameters of high-Tc superconductivity are shown to be connected to the statistics of pairons (hole pairs in their antiferromagnetic (AF) environment) on a square lattice. In particular, we study the density fluctuations and the distribution of the area surrounding each pairon on the scale of the AF correlation length , for the complete range of hole concentration. We show that the key parameters of the phase diagram, the Tc dome, and the pseudogap (PG) temperature , emerge from the statistical properties of the pairon disordered state. In this approach, the superconducting and the PG states appear as inseparable phenomena. The condensation energy, which fixes the critical temperature, is directly proportional to the correlation energy between pairons and not to the energy gap, contrary to conventional superconductors. When the correlation energy between pairons is suppressed by fluctuations, either thermally, by disorder, or in the vortex core, the PG state of disordered pairons is obtained. We attribute the unique features of cuprate superconductivity to this order–disorder transition in real space, which clearly differs from the Bardeen–Cooper–Schrieffer mechanism. Our predictions are in quantitative agreement with low-temperature tunneling and photoemission spectroscopy experiments.

Shock state distributions in porous tantalum and characterization with multipoint velocimetry

Heterogenous materials under shock compression can be expected to reach different shock states throughout the material according to local differences in microstructure and the history of wave propagation. Here, a compact, multiple-beam focusing optic assembly is used with high-speed velocimetry to interrogate the shock response of porous tantalum films prepared through thermal-spray deposition. The distribution of particle velocities across a shocked interface is compared to results obtained using a set of defocused interferometric beams that sampled the shock response over larger areas. The two methods produced velocity distributions along the shock plateau with the same mean, while a larger variance was measured with narrower beams. The finding was replicated using three-dimensional, mesoscopically resolved hydrodynamics simulations of solid tantalum with a pore structure mimicking statistical attributes of the material and accounting for radial divergence of the beams, with agreement across several impact velocities. Accounting for pore morphology in the simulations was found to be necessary for replicating the rise time of the shock plateau. The validated simulations were then used to show that while the average velocity along the shock plateau could be determined accurately with only a few interferometric beams, accurately determining the width of the velocity distribution, which here was approximately Gaussian, required a beam dimension much smaller than the spatial correlation lengthscale of the velocity field, here by a factor of ∼30×, with implications for the study of other porous materials.

A Three-dimensional Model for the Evolution of Magnetohydrodynamic Turbulence in the Outer Heliosphere

We present a time-dependent, three-dimensional single-fluid model for the transport of magnetohydrodynamic (MHD) turbulence that is self-consistently evolving with a dynamic large-scale solar wind in the outer heliosphere. The emphasis is on the region beyond the termination shock, where the solar wind expands subsonically, as well as sub-Alfvénically and nonradially. In extension of earlier work, we refine the treatment of turbulence by considering, in addition to the Elsässer energies, a nonconstant energy difference (or residual energy) and by allowing each of these quantities its own characteristic correlation length scale. While the nonlinear effects in the equations for the Elsässer energies and their length scales are implemented using familiar von Kármán–Howarth style modeling of homogeneous MHD turbulence, the energy difference, which is not conserved in the absence of dissipation, and its length scale are modeled using distinct approaches. We also clarify the impact of the choice of measurement direction for correlation functions associated with two-dimensional fluctuations in transport models. Finally, we illustrate and study the solutions of the resulting six-equation model in detail.

Anatomy of localisation protected quantum order on Hilbert space

Many-body localised (MBL) phases of disordered, interacting quantum systems allow for exotic localisation protected quantum order in eigenstates at arbitrarily high energy densities. In this work, we analyse the manifestation of such order on the Hilbert-space anatomy of eigenstates. Quantified in terms of non-local Hilbert-spatial correlations of eigenstate amplitudes, we find that the spread of the eigenstates on the Hilbert-space graph is directly related to the order parameters which characterise the localisation protected order, and hence these correlations, in turn, characterise the order or lack thereof. Higher-point eigenstate correlations also characterise the different entanglement structures in the many-body localised phases, with and without order, as well as in the ergodic phase. The results pave the way for characterising the transitions between MBL phases and the ergodic phase in terms of scaling of emergent correlation lengthscales on the Hilbert-space graph.

Correlation length of the two-dimensional random field Ising model via greedy lattice animal

For the two-dimensional random field Ising model where the random field is given by independent and identically distributed mean zero Gaussian variables with variance ε2, we study (one natural notion of) the correlation length, which is the critical size of a box at which the influences of the random field and of the boundary condition on the spin magnetization are comparable. We show that as ε→0, at zero temperature the correlation length scales as eΘ(ε−4∕3) (and our upper bound applies for all positive temperatures).

Pairing susceptibility of the two-dimensional Hubbard model in the thermodynamic limit

We compute the diagrammatic expansion of the particle-particle susceptibility via algorithmic Matsubara integration and compute the correlated pairing susceptibility in the thermodynamic limit of the 2D Hubbard Model. We study the static susceptibility and its dependence on the pair momentum $\mathbf{q}$ for a range of temperature, interaction strength, and chemical potential. We show that $d_{x^2-y^2}$-wave pairing is expected in the model in the $U/t\to 0^+ $ limit from direct perturbation theory. From this, we identify key second and third-order diagrams that support pairing processes and note that the diagrams responsible are not a part of charge or spin susceptibility expansions. We find two key components for pairing at momenta $(0,0)$ and $(\pi,\pi)$ that can be well fit as separate bosonic modes. We extract amplitudes and correlation length scales where we find a predominantly local $(\pi,\pi)$ pairing and non-local $\mathbf{q}=(0,0)$ pairs and present the relative weights of these modes for variation in temperature, doping, and interaction strength.

On the Requirements for Inferring Aquifer‐Scale T and S in Heterogeneous Confined Aquifers

AbstractWe study the sensitivity of aquifer‐scale estimates of transmissivity (T) and storativity (S) to the variance and correlation length scale of aquifer heterogeneity, when such estimates are obtained by the traditional approach of analyzing pumping test data. We consider both constant‐rate and variable‐rate pumping tests, and a variety of Theis‐based solution methodologies (single‐ and multiple‐observation well methods, and interpreted single value or transient values for T and S parameters) applied in pumping test data analysis. Our results indicate that achieving reliable inference of effective T and S requires that pumping be continued until the radius of the test‐induced cone of depression exceeds a “representative length” that corresponds to ∼15 times than the correlation length scale of the aquifer heterogeneity. Independent of solution type, pumping history, correlation length scale, magnitude of the sill, and location of observation well, the estimates for T will converge toward the geometric mean. For S, the estimation uncertainty is relatively large for observation wells that are close to the pumping well, but diminishes for observation wells located beyond the representative distance, resulting in convergence to the arithmetic mean. Given that these results have practical implications for how pumping tests should be carried out, we present a simple “rule‐of‐thumb” for estimating the correlation length scale of the heterogeneity of an aquifer.

Characteristic length and curvature of the AOT/brine/squalane “sponge” L3 phases

The effect of salinity (NaCl concentration) was determined at 25 ​°C for systems composed of sodium bis(2-ethylhexyl) sulfosuccinate (AOT) and equal volumes of squalane and brine. At all the NaCl concentrations the samples are triphasic with an upper phase made of pure squalane while brine is present in two other phases. At NaCl concentration (in brine) below 1.6 %w/v there is the coexistence of lamellar and sponge (L3) phases. Loading with NaCl above 1.6 %w/v one observes the coexistence of L3 and pure brine. The amount of AOT dissolved in the AOT bilayer has been quantified by thermogravimetric analysis. At salinity above 2 %w/v of NaCl in brine, the AOT sponge phase shrinks expelling brine and the squalane whose presence in the bilayer becomes negligible. The L3 phases have been further characterized by SAXS and diffusion-NMR. The measured self-diffusion coefficients of water and AOT are essentially coincident with those measured at the same salinity in the absence of squalane. The SAXS curves of sponge phases have been fitted to a single equation accounting for the contributions of the bilayer structure and of the large-scale interactions allowing the determination of the average interpore separation D∗ and the bilayer correlation length ξ. The correlation length has been interpreted as reflecting static randomness of connected bilayer instead of the dynamic thermal undulations. Considering the correlation length as the displacement along the bilayer surface subtending a critical angular change (θ∗) below which the surface appears as flat, permits to define the curvature (H) as |H| =θ∗ξ. The correlation length scales linearly with the square of the bilayer volume fraction as proposed by a previous theoretical model assuming the sponge phases are thermodynamically constrained to a curvature that equals the spontaneous curvature.

Electrostatics of soft (bio)interfaces: Corrections of mean-field Poisson-Boltzmann theory for ion size, dielectric decrement and ion-ion correlations

HypothesisElectrostatics of soft (ion-permeable) (bio)particles (e.g. microorganisms, core/shell colloids) in aqueous electrolytes is commonly formulated by the mean-field Poisson-Boltzmann theory and integration of the charge contributions from electrolyte ions and soft material. However, the effects connected to the size of the electrolyte ions and that of the structural charges carried by the particle, to dielectric decrement and ion-ion correlations on soft interface electrostatics have been so far considered at the margin, despite the limits of the Gouy theory for condensed and/or multivalent electrolytes. ExperimentsAccordingly, we modify herein the Poisson-Boltzmann theory for core/shell (bio)interfaces to include the aforementioned molecular effects considered separately or concomitantly. The formalism is applicable for poorly to highly charged particles in the thin electric double layer regime and to unsymmetrical multivalent electrolytes. FindingsComputational examples of practical interests are discussed with emphasis on how each considered molecular effect or combination thereof affects the interfacial potential distribution depending on size and valence of cations and anions, size of particle charges, length scale of ionic correlations and shell-to-Debye layer thickness ratio. The origins of here-evidenced pseudo-harmonic potential profile and ion size-dependent screening of core/shell particle charges are detailed. In addition, the existence and magnitude of the Donnan potential when reached in the shell layer are shown to depend on the excluded volumes of the electrolyte ions.

Sea ice and snow characteristics from year-long transects at the MOSAiC Central Observatory

Repeated transects have become the backbone of spatially distributed ice and snow thickness measurements crucial for understanding of ice mass balance. Here we detail the transects at the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) 2019–2020, which represent the first such measurements collected across an entire season. Compared with similar historical transects, the snow at MOSAiC was thin (mean depths of approximately 0.1–0.3 m), while the sea ice was relatively thick first-year ice (FYI) and second-year ice (SYI). SYI was of two distinct types: relatively thin level ice formed from surfaces with extensive melt pond cover, and relatively thick deformed ice. On level SYI, spatial signatures of refrozen melt ponds remained detectable in January. At the beginning of winter the thinnest ice also had the thinnest snow, with winter growth rates of thin ice (0.33 m month−1 for FYI, 0.24 m month−1 for previously ponded SYI) exceeding that of thick ice (0.2 m month−1). By January, FYI already had a greater modal ice thickness (1.1 m) than previously ponded SYI (0.9 m). By February, modal thickness of all SYI and FYI became indistinguishable at about 1.4 m. The largest modal thicknesses were measured in May at 1.7 m. Transects included deformed ice, where largest volumes of snow accumulated by April. The remaining snow on level ice exhibited typical spatial heterogeneity in the form of snow dunes. Spatial correlation length scales for snow and sea ice ranged from 20 to 40 m or 60 to 90 m, depending on the sampling direction, which suggests that the known anisotropy of snow dunes also manifests in spatial patterns in sea ice thickness. The diverse snow and ice thickness data obtained from the MOSAiC transects represent an invaluable resource for model and remote sensing product development.

Evidence for growing structural correlation length in colloidal supercooled liquids.

Using video microscopy, we measure the long-time diffusion coefficients of colloidal particles at different concentrations. The measured diffusion coefficients start to deviate from theoretical predictions based on random collision models upon entering the supercooled regime. The theoretical diffusion relation is recovered by assigning an effective mass proportional to the size of structurally correlated clusters to the diffusing particles, providing an indirect method to probe the growth of static correlation length scales approaching the glass transition. This method is tested and validated in the crystallization of mono-disperse colloids in quasi-two-dimensional experiments. The correlation length obtained for a binary colloidal liquid increases by a power law toward a critical packing fraction of ∼0.79. The system relaxation time exhibits a power-law dependence on the correlation length in agreement with dynamical facilitation theories.

Evaluating Latent-Heat-Nudging Schemes and Radar forward Operator Settings for a Convective Summer Period over Germany Using the ICON-KENDA System

Radar data assimilation has been operational at the Deutscher Wetterdienst for several years and is essential for generating accurate precipitation forecasts. The current work attempts to further enhance the radar data assimilation by improving the latent heat nudging (LHN) scheme and by reducing the observation error (OE) caused by the representation error of the efficient modular volume radar operator (EMVORADO). First of all, a series of hindcasts for a one-month convective period over Germany are performed. Compared with radar reflectivity and satellite observations, it is found that the LHN scheme that implicitly adjusts temperature performs better, and the beam broadening effect and the choice of the scattering schemes in EMVORADO are important. Moreover, the Mie scheme with the new parameterization to reduce the brightband effect not only proves to be the best in hindcasts but also that it results in the smallest standard deviations and the shortest horizontal correlation length scales of the OE in data assimilation experiments.